Question: Multiply and simplify the following complex numbers: $({-1-3i}) \cdot ({-1+i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-3i}) \cdot ({-1+i}) = $ $ ({-1} \cdot {-1}) + ({-1} \cdot {i}) + ({-3i} \cdot {-1}) + ({-3i} \cdot {i}) $ Then simplify the terms: $ (1) + (-i) + (3i) + (-3i^2) $ Imaginary unit multiples can be grouped together. $ 1 + (-1 + 3)i - 3 i^2 $ After we plug in $i^2 = -1$, the result becomes $ 1 + (-1 + 3)i - (-3) $ The result is simplified: $ (1 + 3) + (2i) = 4+2i $